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  <div class="question_difficulty">
   难度：Easy
  </div>
  <div>
   <h1 class="question_title">
    1010. Powerful Integers
   </h1>
   <p>
    Given two positive integers
    <code>
     x
    </code>
    and
    <code>
     y
    </code>
    , an integer is
    <em>
     powerful
    </em>
    &nbsp;if it is equal to
    <code>
     x^i + y^j
    </code>
    &nbsp;for&nbsp;some integers
    <code>
     i &gt;= 0
    </code>
    and
    <code>
     j &gt;= 0
    </code>
    .
   </p>
   <p>
    Return a list of all
    <em>
     powerful
    </em>
    integers that have value less than or equal to
    <code>
     bound
    </code>
    .
   </p>
   <p>
    You may return the answer in any order.&nbsp; In your answer, each value should occur at most once.
   </p>
   <p>
    &nbsp;
   </p>
   <div>
    <p>
     <strong>
      Example 1:
     </strong>
    </p>
    <pre>
<strong>Input: </strong>x = <span id="example-input-1-1">2</span>, y = <span id="example-input-1-2">3</span>, bound = <span id="example-input-1-3">10</span>
<strong>Output: </strong><span id="example-output-1">[2,3,4,5,7,9,10]</span>
<strong>Explanation: </strong>
2 = 2^0 + 3^0
3 = 2^1 + 3^0
4 = 2^0 + 3^1
5 = 2^1 + 3^1
7 = 2^2 + 3^1
9 = 2^3 + 3^0
10 = 2^0 + 3^2
</pre>
    <div>
     <p>
      <strong>
       Example 2:
      </strong>
     </p>
     <pre>
<strong>Input: </strong>x = <span id="example-input-2-1">3</span>, y = <span id="example-input-2-2">5</span>, bound = <span id="example-input-2-3">15</span>
<strong>Output: </strong><span id="example-output-2">[2,4,6,8,10,14]</span>
</pre>
    </div>
   </div>
   <p>
    &nbsp;
   </p>
   <p>
    <strong>
     Note:
    </strong>
   </p>
   <ul>
    <li>
     <code>
      1 &lt;= x &lt;= 100
     </code>
    </li>
    <li>
     <code>
      1 &lt;= y&nbsp;&lt;= 100
     </code>
    </li>
    <li>
     <code>
      0 &lt;= bound&nbsp;&lt;= 10^6
     </code>
    </li>
   </ul>
  </div>
  <div>
   <h1 class="question_title">
    1010. 强整数
   </h1>
   <p>
    给定两个正整数
    <code>
     x
    </code>
    和
    <code>
     y
    </code>
    ，如果某一整数等于
    <code>
     x^i + y^j
    </code>
    ，其中整数&nbsp;
    <code>
     i &gt;= 0
    </code>
    且&nbsp;
    <code>
     j &gt;= 0
    </code>
    ，那么我们认为该整数是一个
    <em>
     强整数
    </em>
    。
   </p>
   <p>
    返回值小于或等于&nbsp;
    <code>
     bound
    </code>
    &nbsp;的所有
    <em>
     强整数
    </em>
    组成的列表。
   </p>
   <p>
    你可以按任何顺序返回答案。在你的回答中，每个值最多出现一次。
   </p>
   <p>
    &nbsp;
   </p>
   <p>
    <strong>
     示例 1：
    </strong>
   </p>
   <pre><strong>输入：</strong>x = 2, y = 3, bound = 10
<strong>输出：</strong>[2,3,4,5,7,9,10]
<strong>解释： </strong>
2 = 2^0 + 3^0
3 = 2^1 + 3^0
4 = 2^0 + 3^1
5 = 2^1 + 3^1
7 = 2^2 + 3^1
9 = 2^3 + 3^0
10 = 2^0 + 3^2
</pre>
   <p>
    <strong>
     示例&nbsp;2：
    </strong>
   </p>
   <pre><strong>输入：</strong>x = 3, y = 5, bound = 15
<strong>输出：</strong>[2,4,6,8,10,14]
</pre>
   <p>
    &nbsp;
   </p>
   <p>
    <strong>
     提示：
    </strong>
   </p>
   <ul>
    <li>
     <code>
      1 &lt;= x &lt;= 100
     </code>
    </li>
    <li>
     <code>
      1 &lt;= y&nbsp;&lt;= 100
     </code>
    </li>
    <li>
     <code>
      0 &lt;= bound&nbsp;&lt;= 10^6
     </code>
    </li>
   </ul>
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